# young's modulus vs longitudal deformation modulus

Young's modulus is typiccaly denoted with E. I have come accross a similar quantity called longitudal deformation modulus (in Russian literature, they call it модуль продольных деформаций) and it is denoted D. What is that quantity and is it the same as Young's modulus?

• Show us some equations using your D. Then non-Russian-speaking engineers might be able to answer the question. Aug 6, 2018 at 0:42

Young's modulus is the elastic constant for a bar of a finite thickness which is free to contract or expand laterally as it is stretched lengthwise. In terms of the Lame' constants $\lambda$ and $\mu$ (see https://en.wikipedia.org/wiki/Lamé_parameters) we have $$E= \lambda(1-2\sigma)+2\mu=\mu \frac{3\lambda+2\mu}{\lambda+\mu}$$ where $$\sigma=\frac 12 \frac \lambda{\lambda+\mu}$$ is Poisson's ratio --- the ratio of lateral contraction to lengthways stretching. The elastic constant for longitudinal stretching of a sytem that is not allowed to shrink sideways as it is stretched - for example the longitudinal "p" waves in an earthquake --- is different. It is given by $\lambda+2\mu$, so the velocity of longitudinal $p$-waves is $$V_p = \sqrt{\frac{\lambda+2\mu}{\rho}}$$ where $\rho$ is the density.
• If this is what the Russian text means, then the longitudinal modulus is related to $E$ and $\nu$ both of which are easy to measure in a uniaxial compression (or tension) test. The relationship would be something like $D = \dfrac{E}{1-\nu^2}$ - if this really is the meaning of $D$, of course. Aug 6, 2018 at 0:42